Solve for $x$ : $x^2 - 19x + 90 = 0$
Explanation: The coefficient on the $x$ term is $-19$ and the constant term is $90$ , so we need to find two numbers that add up to $-19$ and multiply to $90$ The two numbers $-9$ and $-10$ satisfy both conditions: $ {-9} + {-10} = {-19} $ $ {-9} \times {-10} = {90} $ $(x {-9}) (x {-10}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -9) (x -10) = 0$ $x - 9 = 0$ or $x - 10 = 0$ Thus, $x = 9$ and $x = 10$ are the solutions.